# What Makes Airplanes Fly? History, Science and Applications ofAerodynamics

## CONTENTS OF CURRICULUM UNIT 90.07.10

- Narrative
- I. Introduction
- II. Rationale and General Objectives of the Unit
- III. Historical Overview of the Development of Aircraft4
- IV. The Mathematical Application
- II. An Introduction to Graph Theory
- Sample Lesson Plan 1
- Sample Lesson plan 2
- Sample Lesson Plan 3
- Sample Lesson Plan 4
- Sample Problems For Class Discussion
- Bibliography

### Unit Guide

## Historical Developments of the Aircraft Industry with Mathematical Applications

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## Sample Lesson plan 2

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Topic: The airplane problem revisited.
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Objectives: Students will be able
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- a) to draw a model for the problem
- b) to identify a critical path.
- c) to find a solution for the problem

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Prerequisites:
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- a) to draw a graph or a digraph.

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Skills and Concepts presented:
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- a) Organization of data.
- b) Constructing an Activity Analysis Digraph.
- c) Finding the critical path.

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Developments:
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- 1. Review nodes, vertices and edges.
- 2. Review drawing graphs.
- 3. Re-introduce the airplane problem.
- 4. Organize the information in a table.
- 5. Discuss the reasons for a starting and ending position.
- 6. Introduce the method of making “The Activity Analysis Digraph.
- 7. Draw a graph from the information (have students suggest possible order in which the activities can be done).
- 8. Introduce the words critical paths. Discuss all the possible paths.
- 9. Have students suggest possible answers.

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Extension Activities:
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Draw an activity analysis digraph for this job. Find the shortest possible time that these tasks will take.

- 1. Have students suggest tasks that they would like to represent using an activity digraph.
- 2. Draw an activity digraph for a person getting ready to go on vacation.
- 3. Draw an activity digraph for the activities of the air hostesses during the flight.
- 4. A group of girls decided to cook lunch for some friends. The activities were:

A. clean house 30 mins B. Decide on menu 15 mins C. Purchase food 60 mins D. Cook food 50 mins E. Set table 10 mins F. Place cooked 5 mins food on table.